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a,b,c, and d are the position vectors of four coplanar points such that (a-d).(b-c)=(b-d).(c-a)=0 . Show that the point d represents the orthocentre of the triangle with a,b and c as its vertices

a,b,c, and d are the position vectors of four coplanar points such that (a-d).(b-c)=(b-d).(c-a)=0  .  Show that the point d represents the orthocentre of the triangle with a,b and c as its vertices

Grade:12th pass

1 Answers

Arun
25758 Points
4 years ago
Dear student
 
First equation means that
AD\perp BC
Second equation means
BD \perp CA
Then D is the intersection of altitudes through A and B. Hence D is orthocentre.

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